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[Equations describing fluid motion, and some of their simpler solutions, can be found in particular in Sect. 1 of the book by Monin and Yaglom (1971) (later referred as MYl). It is also pointed out there that these solutions do not by any means always correspond to a flow that may actually be observed. Thus, it is noted in Sect. 1.3 of MY1 that the flow in a tube corresponds to the classical Hagen-Poiseuille solution described by Eqs. (1.23–1.26) (all the references to equations beginning with the digit 1 relate to Sect. 1 of MYl) only in the case of sufficiently high viscosity and sufficiently low mean velocity. Similarly, in Sect. 1.4 of MY1 it was stressed that the Blasius solution of the boundary-layer equation on a flat plate gives good agreement with the data only in the case of fairly small values of Ux/v. The same is true for all other examples of fluid flows. Taking the case of time-independent boundary conditions for simplicity, we find that corresponding to them time-independent boundry conditions for simplicity, we find that corresponding to them time-independent solutions of the equations of fluid mechanics, whether exact or approximate, give a satisfactory description of real flows only under certain special conditions. If these conditions are not met, the nature of the flow undergoes a sharp change, and instead of a regular smooth variation of the fluid mechanical quantities in space and time, we observe irregular fluctuations of all these quantities, having very complex nature as illustrated in Fig. 2.1 of MY1. Thus, flows of fluid may be divided into two very different classes: smooth, quiet flows which vary in time only when the external conditions or the forces acting are changing, known as laminar flows; and flows accompanied by irregular fluctuations of all the fluid mechanical quantities in time and space, which are called turbulent flows.]
Published: Dec 17, 2012
Keywords: Linear Stability Theory; Circular Poiseuille Flow; Wave-like Disturbances; Plane-parallel Flow; Neutral Curve
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